Fig. 4: Entanglement of long-lived hf qubits and midcircuit QND read-out.

a, Measurement of the conditional phase accrued by Rb atoms undergoing a π-2π-π sequence (eye diagram). The Cs atoms were prepared in the eigenstates \(\left\vert 0\right\rangle\) or \(\left\vert 1\right\rangle\) (dashed boxes). The conditional phase was 1.01(1)π, and the SPAM-corrected contrast was 0.88(1). The gr pulses implemented a hf CZ gate up to single-qubit phases. The dashed grey line indicates the point of maximal contrast. Spin echoes (\({\pi }_{-{\rm{y}}}^{{\rm{hf}}}\)) are incorporated to mitigate hf dephasing, with π pulses around the −y axis. b, Parallel preparation of the canonical Bell state \(\left\vert {\varPsi }^{+}\right\rangle\) across several Rb–Cs pairs. By measuring the populations and coherences (dashed boxes), we extracted an average SPAM-corrected Bell state fidelity of \({{\mathcal{F}}}_{{\rm{Bell}}}=0.69(3)\). The combination of hf π/2-pulses and gr pulses realized a CNOT operation up to single-qubit rotations. The phase correction c corresponds to the point of maximal contrast in a. c, Example Cs MCR histogram as used for d and e (7 ms fluorescence; Supplementary Information Section 2). The fitted discrimination fidelity was 0.990(3). d, After preparing the Bell state \(\left\vert {\varPsi }^{{\rm{x}}}\right\rangle\) (see text), the MCR of the Cs atoms projects the two-qubit state. Conditioning on the measurement outcomes reveals 〈ZX〉_Cs,Rb correlations, which confirm that the Rb coherence survives MCR. The conditional phase was 1.02(1)π, and the SPAM-corrected contrast was 0.68(1). DD denotes dynamical decoupling, and Π₀₍₁₎ denotes measurement of the 0(1) outcome on the Cs qubit. e, Auxiliary-based QND measurement of the Rb qubit through the Cs qubit. The read-out fidelity was extracted as \({{\mathcal{F}}}_{{\rm{QND}}}=0.76(2)\).